As I am not a native English speaker, I sometimes am bothered a little with the word "monoid", which is by definition a semigroup with identity. But why this terminology?

I searched some dictionaries (Longman for English, Larousse for Francais, Langenscheidts for Dentsch) but didn't find any result, and it seems to me that it is just a pronounciable word with certain mathematical meaning. So, where does it come from? Is there any etymological explanation? Who was the first mathematician who used it?

A couple of thoughts: a monoid is a structure with just ONE operation, and another name was needed other than group, semi-group, etc. Secondly, a monoid is, essentially, the same thing as a category with a SINGLE object. (Wikipedia)
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Old JohnJun 11 '12 at 12:54

4 Answers
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For what it is worth, the Oxford English Dictionary traces monoid in this sense back to Chevalley's Fundamental Concept of Algebra published in 1956. Arthur Mattuck's review of the book in 1957 suggests that this use may be new, or at least new enough to be not in common mathematical parlance.

Edit:

Indeed, as recently as 1954 we've seen some use of the term "monoid" to mean a semigroup, not necessarily one with identity.

According to the OED again, the use of the word monoid in algebraic geometry (to denote "a surface which possesses a conical point of the highest possible order") dates back to 1866, and likely predates the use of the same term as semigroup with identity.

Much of the book is available on Google, including page 4, where Chevalley defines monoid. He doesn't give any motivation on that page.
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Gerry MyersonJun 11 '12 at 13:31

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It seems the word "monoid" does not appear in Volume II of Clifford and Preston's seminal work "The Algebraic Theory of Semigroups" (1967), but it is in the late John Howie's text "An Introduction to Semigroup Theory" (1975). So, it seems to have gone from obscurity to common usage somewhere in these 8 years.
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user1729Jun 11 '12 at 13:38

@Gerry: indeed. And I am not even sure whether Chevalley was the first one to put that term in print in its modern meaning, I'm just trying to give an indication of a possible answer (or some line to track) to the last question in the original post above.
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Willie WongJun 11 '12 at 13:39

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@user1729 I think we can back the date of common usage up to 1971, since MacLane's Categories for the Working Mathematician uses it casually.
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rschwiebJun 11 '12 at 14:10

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@rschwieb: It is, perhaps, interesting that in the 1954 review, quoted in the post, it is Clifford reviewing and he pointedly does not use the word "monoid". So maybe he was against the word and didn't include it in his book for this reason, not because it wasn't in common usuage.
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user1729Jun 11 '12 at 14:18

If Chevalley was the first to popularize the term "monoid", then I can pretty confidently guess that it meant the structure of operators on a single type (i.e., a category with a single object). Note that Chevalley's second example (after the mandatory natural numbers) is the collection of mappings from a set to itself. His term for the monoid operation is "composition."

The term "groupoid" in the sense of a category with invertible arrows was already well-established. So, the use of "monoid" to mean a category of arrows on a single object seems quite natural.

μόνος, -η, -ον (monos).
In ancient greek means 'alone' or 'single. The 'monoid' in abstract algebra is a structure with a single binary operation. Single in ancient greek can be translated with the word 'monos', from which, the word 'monoid'